- #1
tmpr
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If the magnitude of acceleration is constant, and acceleration is perpendicular to velocity, is speed constant? Also, is speed not constant when the magnitude of acceleration is not constant? How would I show this?
I tried to do this:
If position is [tex]p(t)=(x(t),y(t))[/tex], then velocity is [tex]p'(t)=(x'(t),y'(t))[/tex] and acceleration is [tex]p''(t)=(x''(t),y''(t))[/tex]. If the magnitude of acceleration is constant, [tex]|p''(t)|=k[/tex]. If acceleration and velocity are perpendicular, [tex]p'(t) \cdot p''(t) = x'(t)x''(t) + y'(t)y''(t) = 0 [/tex].
But I'm stuck here.
How do I show [tex]|p'(t)|=c[/tex] for some constant?
I tried to do this:
If position is [tex]p(t)=(x(t),y(t))[/tex], then velocity is [tex]p'(t)=(x'(t),y'(t))[/tex] and acceleration is [tex]p''(t)=(x''(t),y''(t))[/tex]. If the magnitude of acceleration is constant, [tex]|p''(t)|=k[/tex]. If acceleration and velocity are perpendicular, [tex]p'(t) \cdot p''(t) = x'(t)x''(t) + y'(t)y''(t) = 0 [/tex].
But I'm stuck here.
How do I show [tex]|p'(t)|=c[/tex] for some constant?